Question

Convert the following temperatures to Fahrenheit degrees. a. \(-5^{\circ} \mathrm{C}\) b. \(273 \mathrm{K}\) c. \(-196^{\circ} \mathrm{C}\) d. \(0 \mathrm{K}\) e. \(86^{\circ} \mathrm{C}\) f. \(-273^{\circ} \mathrm{C}\)

Short answer

a. \(23^{\circ} \mathrm{F}\)

Step-by-step solution

a. Convert -5°C to Fahrenheit.#

Using the Celsius to Fahrenheit formula: \[F = \frac{9}{5}(-5) + 32\] Calculate the result: \[F = -9 + 32\] \[F = 23\] The temperature is 23°F.

Key concepts

Celsius to Fahrenheit

Understanding the conversion from Celsius to Fahrenheit is essential because these two temperature scales are widely used in daily life and scientific contexts. The formula to convert Celsius to Fahrenheit is:
\[ F = \frac{9}{5}C + 32 \].
Here, \( F \) represents the temperature in degrees Fahrenheit, and \( C \) is the temperature in degrees Celsius. To apply this formula, you start by multiplying the Celsius temperature by 9/5 (or 1.8) and then add 32 to the result. For example, let's convert -5°C to Fahrenheit:
\[ F = \frac{9}{5}(-5) + 32 \]
\[ F = -9 + 32 \]
The answer is \( F = 23°F \), which means -5°C is equal to 23°F. It's worth noting that the point where Celsius and Fahrenheit scales intersect is -40 degrees, meaning -40°C is equal to -40°F. Understanding this conversion allows students to easily switch between the two temperature measurements.

Temperature Scales

Temperature scales provide a way to quantify the warmth or coldness of an object or environment. The three primary temperature scales used in science and everyday life are Celsius (°C), Fahrenheit (°F), and Kelvin (K).

• Celsius: Predominantly used in most countries around the world, and for scientific purposes. Water freezes at 0°C and boils at 100°C under standard atmospheric conditions.
• Fahrenheit: Mainly used in the United States and some Caribbean countries. On this scale, water freezes at 32°F and boils at 212°F under standard atmospheric conditions.
• Kelvin: The Kelvin scale is the SI unit for temperature and is used extensively in the scientific community. Unlike Celsius and Fahrenheit, it does not use degrees. Instead, it starts at absolute zero, the theoretical lowest possible temperature. Water freezes at 273.15K and boils at 373.15K under standard atmospheric conditions.

While Celsius and Fahrenheit scales are degree-based and include negative numbers, the Kelvin scale is an absolute scale where 0 K represents the absence of all thermal energy. Familiarity with these scales and how to convert between them is a critical skill for students in many fields of study.

Kelvin to Fahrenheit

Kelvin to Fahrenheit conversion is a two-step process involving a conversion from Kelvin to Celsius, followed by Celsius to Fahrenheit. The general formula for converting Kelvin to Celsius is:
\[ C = K - 273.15 \]
Then, as previously discussed, you convert Celsius to Fahrenheit. If you wanted to convert 273K to Fahrenheit, first convert Kelvin to Celsius:
\[ C = 273 - 273.15 \]
\[ C = -0.15^{\text{°C}} \]
Following the conversion to Celsius, you then apply the Celsius to Fahrenheit formula:
\[ F = \frac{9}{5}(-0.15) + 32 \]
\[ F = -0.27 + 32 \]
\[ F = 31.73^{\text{°F}} \]
Understanding how to perform these conversions is not only useful for scientific and educational purposes but it is also practical for interpreting weather reports, cooking, and international travel where different temperature scales may be used.